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Abstract We prove a functional transcendence theorem for the integrals of algebraic forms in families of algebraic varieties. This allows us to prove a geometric version of André’s generalization of the Grothendieck period conjecture, which we state using the formalism of Nori motives. More precisely, we prove a version of the Ax–Schanuel conjecture for the comparison between the flat and algebraic coordinates of an arbitrary admissible graded polarizable variation of integral mixed Hodge structures. This can be seen as a generalization of the recent Ax–Schanuel theorems of [13, 18] for mixed period maps.
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Cohomology of cluster varieties II: Acyclic case
Abstract In the previous work, we initiated the study of the cohomology of locally acyclic cluster varieties. In the present work, we show that the mixed Hodge structure and point counts of acyclic cluster varieties are essentially determined by the combinatorics of the independent sets of the quiver. We use this to show that the mixed Hodge numbers of acyclic cluster varieties of really full rank satisfy a strong vanishing condition.
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- PAR ID:
- 10478563
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Journal of the London Mathematical Society
- Volume:
- 108
- Issue:
- 6
- ISSN:
- 0024-6107
- Format(s):
- Medium: X Size: p. 2377-2414
- Size(s):
- p. 2377-2414
- Sponsoring Org:
- National Science Foundation
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